Comparison of elasticity patterns of elasmobranchs and mammals with
review of vital parameters of lamnids
Henry F. Mollet, Moss Landing Marine Labs and Monterey Bay Aquarium:
Abstract:
Vital parameters (age-at-first-reproduction, maximum-reproductive-age, age-specific
fertilities, and age-specific mortalities) of lamnids were reviewed. Despite
progress in the last 20 years, vital parameters of lamnids and many other elasmobranchs
are not sufficiently well-known to produce reasonably accurate population growth
rates (lambda). Luckily, the elasticity pattern of a species that is needed
to evaluate management proposals is fairly robust and does not require an accurate:lambda.
Furthermore, there is no need to calculate lambda because the elasticity pattern
is determined by age-at-first-reproduction (alpha) and generation time (Abar)
alone, with gestation period (GP) providing a refinement: E(fertility) = E1
= 1/Abar; E(juvenile survival) = E2 = (alpha - GP) E1; E(adult survival) = E3
= 1 - E2 = (Abar - alpha + GP) E1. These are lower-level elasticities of the
vital parameters as they appear in a life history table and E2 includes survival
to age one. Therefore, they do not sum to one but are easily normalized. The
exclusion of survival to age one from E2 distorts the elasticity pattern, in
particular for species with low age-at-first-reproduction (alpha < 2). Abar
is usually not known. However, using an Abar estimate based on the mean Abar/alpha
ratio of 60 elasmobranchs (1.31, coefficient of variation 9.3%, range 1.1-1.8)
provided promising results. The elasticity pattern of elasmobranchs as a function
of age-at-first-reproduction indicated that E2 is largest for all elasmobranchs
if alpha > 1 yr (valid for most if not all elasmobranchs). Accordingly, protection
of juveniles will provide the most effective measure to reverse population declines
if that has been observed for an elasmobranch species. The mean Abar/alpha ratio
of 50 mammals (2.44, coefficient of variation 33.5%, range 1.2-5.0) is larger
and more variable compared to that of elasmobranchs and, accordingly, their
elasticity patterns are more complicated.